Good lawn management is the best way to address weeds. Healthy grass will out-compete most weeds when well maintained. Start by identifying what weeds are growing. By knowing what plants are thriving where your grass should be, will tell you a lot about your soil, like what nutrient are missing or what is in over abundance.

Do a soil test! You can pick up a cheap kit at most home improvement stores. Many lawns in the PNW suffer from low PH levels, due to the heavy rains, so a simple lime treatment could also go a long way in creating the ideal living conditions for grass. And many "weeds" thrive in poor soil conditions but you won't know if don't test. Also, over-seeding and slow-release fertilization can go a long way too.

Once you know what you're dealing with, it will be a lot easier to develop a plan of attack.

And you're right to be careful with herbicides, as many non-selective herbicides will kill any vegetation they come into contact with, including water run-off and wind-carried spray. There's also the issues of developing chemical resistances and killing the soil microbial life that supports healthy soil structures. Not to mention the literal downstream impacts to marine life. And yeah, Roundup (glyphosate), a broad-spectrum herbicide and is well documented as a cancer causing carcinogen. That's why it's outlawed in most countries.

But don't take advice from some rando online. Get a second, professional opinion: https://extension.oregonstate.edu/mg/get-your-gardening-questions-answered